This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370336 #13 Feb 24 2024 05:58:13
%S A370336 1,5,-25,300,-3000,34375,-426750,5539375,-73968750,1010175000,
%T A370336 -14043011250,198006675000,-2824523453125,40684553625000,
%U A370336 -590871274218750,8642318714253125,-127185323309250000,1881843237600000000,-27976771190059687500,417688301999460937500,-6259735680122821875000
%N A370336 Expansion of [ Sum_{n>=0} 5^n * (2*4^n + 1)/3 * x^(n*(n+1)/2) ]^(1/3).
%C A370336 Self-convolution cube equals A370335.
%H A370336 Paul D. Hanna, <a href="/A370336/b370336.txt">Table of n, a(n) for n = 0..630</a>
%F A370336 a(n) ~ (-1)^(n+1) * c * d^n / n^(4/3), where d = 16.061038491618401040959460250524051290971925631740259277535... and c = 0.25648790376068702946627569573532916303248367815529074... - _Vaclav Kotesovec_, Feb 24 2024
%e A370336 G.f.: A(x) = 1 + 5*x - 25*x^2 + 300*x^3 - 3000*x^4 + 34375*x^5 - 426750*x^6 + 5539375*x^7 - 73968750*x^8 + 1010175000*x^9 - 14043011250*x^10 + ...
%e A370336 RELATED SERIES.
%e A370336 The cube of the g.f. A(x) yields the g.f. of A370335 starting as
%e A370336 A(x)^3 = 1 + 15*x + 275*x^3 + 5375*x^6 + 106875*x^10 + 2134375*x^15 + 42671875*x^21 + 853359375*x^28 + 17066796875*x^36 + ... + 5^n*(2*4^n + 1)/3 * x^(n*(n+1)/2) + ...
%o A370336 (PARI) {a(n) = my(A);
%o A370336 A = sum(m=0, sqrtint(2*n+1), 5^m*(2*4^m + 1)/3 * x^(m*(m+1)/2) +x*O(x^n))^(1/3);
%o A370336 polcoeff(H=A, n)}
%o A370336 for(n=0, 20, print1(a(n), ", "))
%Y A370336 Cf. A370335, A370016.
%K A370336 sign
%O A370336 0,2
%A A370336 _Paul D. Hanna_, Feb 23 2024